A homeomorphism classification of wildly imbedded two-spheres in S³

Fred Rex Sinal

Vol. 77 (1978), No. 1, 255–271

DOI: 10.2140/pjm.1978.77.255

Abstract

If a two-manifold M is wildly imbedded S³, it gives rise to a pair of noncompact three-manifolds of a special type. This type is considered in detail and a homeomorphism classification theorem for it is derived. This result is then used to decide whether there is a homeomorphism of S³ to itself, which takes M onto another, given two-manifold.

Mathematical Subject Classification 2000

Primary: 57N12

Secondary: 57M30, 57N40

Milestones

Received: 11 May 1977

Revised: 19 October 1977

Published: 1 July 1978